diff --git a/tests/test_exceptions.py b/tests/test_exceptions.py
new file mode 100644
index 000000000..c2700e70f
--- /dev/null
+++ b/tests/test_exceptions.py
@@ -0,0 +1,88 @@
+import io
+from contextlib import redirect_stdout
+
+import jax
+import jax.numpy as jnp
+import jaxlib.xla_extension
+import pytest
+
+from jaxsim import exceptions
+
+
+def test_exceptions_in_jit_functions():
+
+    msg_during_jit = "Compiling jit_compiled_function"
+
+    @jax.jit
+    def jit_compiled_function(data: jax.Array) -> jax.Array:
+
+        # This message is compiled only during JIT compilation.
+        print(msg_during_jit)
+
+        # Condition that will trigger the exception.
+        failed_if_42_plus = jnp.allclose(data, 42)
+
+        # Raise a ValueError if the condition is met.
+        # The fmt string is built from kwargs.
+        exceptions.raise_value_error_if(
+            condition=failed_if_42_plus,
+            msg="Raising ValueError since data={num}",
+            num=data,
+        )
+
+        # Condition that will trigger the exception.
+        failed_if_42_minus = jnp.allclose(data, -42)
+
+        # Raise a RuntimeError if the condition is met.
+        # The fmt string is built from args.
+        exceptions.raise_runtime_error_if(
+            failed_if_42_minus,
+            "Raising RuntimeError since data={}",
+            data,
+        )
+
+        return data
+
+    # In the first call, the function will be compiled and print the message.
+    with jax.log_compiles():
+        with io.StringIO() as buf, redirect_stdout(buf):
+
+            data = 40
+            out = jit_compiled_function(data=data)
+            stdout = buf.getvalue()
+            assert out == data
+
+    assert msg_during_jit in stdout
+    assert jit_compiled_function._cache_size() == 1
+
+    # In the second call, the function won't be compiled and won't print the message.
+    with jax.log_compiles():
+        with io.StringIO() as buf, redirect_stdout(buf):
+
+            data = 41
+            out = jit_compiled_function(data=data)
+            stdout = buf.getvalue()
+            assert out == data
+
+    assert msg_during_jit not in stdout
+    assert jit_compiled_function._cache_size() == 1
+
+    # Let's trigger a ValueError exception by passing 42.
+    # Note: the real ValueError is printed in a stream that I couldn't figure out
+    # how to capture in pytest.
+    with pytest.raises(jaxlib.xla_extension.XlaRuntimeError):
+
+        data = 42
+        _ = jit_compiled_function(data=data)
+
+    assert jit_compiled_function._cache_size() == 1
+
+    # Let's trigger a RuntimeError exception by passing -42.
+    # Note: the real RuntimeError is printed in a stream that I couldn't figure out
+    # how to capture in pytest.
+    with pytest.raises(jaxlib.xla_extension.XlaRuntimeError):
+
+        data = -42
+        _ = jit_compiled_function(data=data)
+
+    assert jit_compiled_function._cache_size() == 1